DOCUMENTO CEDE 2006-24
ISSN 1657-7191 (Edición Electrónica)
JULIO DE 2006
CEDE
INSTITUTIONS INFLUENCE PREFERENCES:
EVIDENCE FROM A COMMON POOL RESOURCE EXPERIMENT
CARLOS RODRÍGUEZ-SICKERT
RICARDO ANDRÉS GUZMÁN*
JUAN CAMILO CÁRDENAS §
Abstract
We model the dynamic effects of external enforcement on the exploitation of a
common pool resource. Fitting our model to the results of experimental data we
find that institutions influence social preferences. We solve two puzzles in the
data: the increase and later erosion of cooperation when commoners vote
against the imposition of a fine, and the high deterrence power of low fines.
When fines are rejected, internalization of a social norm explains the increased
cooperation; violations (accidental or not), coupled with reciprocal preferences,
account for the erosion. Low fines stabilize cooperation by preventing a spiral of
negative reciprocation.
Keywords: field experiments, common-pool resources, cooperation,
enforcement, regulation, social preferences, social norms, learning models.
JEL Classification: C93, D01, D64, D83, H4, H3, Q28
*
Corresponding author. Instituto de Economía, Facultad de Ciencias Económicas y Administrativas,
Pontificia Universidad Católica de Chile. Avda. Vicuña Mackenna 4860, Macul, Santiago, Chile. Tel. (56 2)
354-4303. Fax (56 2) 553-2377. E-mail: [email protected].
§
We are deeply indebted to Sam Bowles, Rajiv Sethi, Marcos Singer, Rodrigo Harrison, Rodrigo Troncoso,
Bob Rowthorn and Will Mullins. Their unconditional cooperation substantially improved this paper.
LAS INSTITUCIONES INFLUENCIAN LAS PREFERENCIAS:
EVIDENCIA EN UN EXPERIMENTO DE RECURSOS COMUNES
Resumen
En este artículo modelamos los efectos dinámicos del monitoreo y control
externo en la explotación de un recursos de uso común. Al contrastar un modelo
de preferencias con los resultados de datos experimentales encontramos que las
instituciones afectan las preferencias. Con los datos empíricos intentamos
resolver dos preguntas: el aumento y erosión posterior de la cooperación cuando
los usuarios del recurso votan contra la imposición de una sanción, y el efecto
positivo de las multas o sanciones bajas. Cuando las multas son rechazadas en
una votación, la internalización de las normas sociales explica el aumento de la
cooperación; las violaciones a las reglas (voluntarias o no), en conjunto con las
preferencias por la reciprocidad, explican la erosión de la cooperación. Las
multas o sanciones bajas estabilizan la cooperación al prevenir un espiral de
reciprocidad negativa.
Palabras clave: experimentos económicos en campo, recursos de uso común,
cooperación, cumplimiento de regulaciones, regulación, preferencias sociales,
normas sociales, modelos de aprendizaje.
Clasificación JEL: C93, D01, D64, D83, H4, H3, Q28
2
1.
INTRODUCTION
It is now widely agreed that social preferences, such as altruism, reciprocity, and
guilt, are strong motives for behavior. Without a state to enforce property rights (or the
disciplining hand of reputation) the selfish homo economicus engages in a war of all
against all. Not the homo sapiens: social preferences help him avert chaos and
cooperate.
Economists usually assume away the influence institutions exert on social
preferences. Often the assumption is harmless, but occasionally it may result in
unexpected or even disastrous consequences. English health authorities learned this the
hard way. They decided to promote blood donations by paying donors. Instead of
increasing, blood donations plummeted (Titmuss 1969).1
Experiments indicate institutions affect social preferences. For example, Gneezy
and Rustichini (2000) studied day-care centers in Haifa, where a fine was imposed on
parents who picked up their children late. Unexpectedly, tardiness more than doubled in
those centers. A plausible explanation is that, by transforming a misdemeanor into a
commodity that parents could buy cheaply, the fine eroded their sense of duty. Another
example is Falk and Kosfeld’s (2004) experimental study of principal-agent relations.
They gave principals the option to set a lower bound on the effort of agents. Falk and
Kosfeld found that agents who were not restricted by their principals worked harder than
those who were. Agents punished distrust.
In this paper we explore the dynamic effects of external enforcement on the
exploitation of a common pool resource (CPR).2 As the previous evidence suggests,
external enforcement may change the preferences of players. Thus, we begin by
developing a model of CPR games that captures that possibility. The ingredients of the
model are:
1
See Bowles (1998, 2005) for an extensive discussion of endogenous preferences and their policy
implications.
2
In a CPR game each player chooses privately how many tokens she will extract from a common pool. A
player’s material payoff depends positively on the number of tokens she extracts and negatively on the
aggregate level of extraction. Thus, individual and social interest conflict.
3
1. Heterogeneous preferences. We distinguish three types of players: (i) selfish,
who only care about their own material payoffs; (ii) unconditional cooperators,
who feel guilty when they violate a social norm; (iii) conditional cooperators, who
experience guilt with an intensity that declines when others violate the norm.
2. State-dependent preferences. When institutions change, player types may
change as well. Institutions comprise such things as the enforcement of a norm
by an external authority.
3. Stochastic behavior. A player will choose with higher probability those actions
that give her a higher expected utility.
4. Adaptive expectations. Each player has an estimate of how much her peers will
extract from the common pool, and updates that estimate as she observes what
they actually do.
Next, we fit our model to experimental data. In our experiment, groups of five
persons played a CPR game twenty times. In some treatments the experimenter fined
players he caught extracting more than one token (he applied the fines in private to
prevent shame from affecting behavior). Some groups were treated with a high fine,
other groups with a low one. Both fines induced high levels of cooperation. The effect of
the high fine accorded with our expectations. The deterrence power of the low fine, by
contrast, could not be justified by any reasonable parameterization of selfish
preferences. Even more surprising was what happened when the experimenter
proposed the sanction mechanism to the players but they voted against it. Extraction fell
sharply at first, and then cooperation slowly unraveled back to its original low level.3 One
may infer the norm was internalized by some players even when it was not enforced.
Without enforcement, moralization seemed to vanish over time.
3
Ostrom, Gardner and Walker (1994) and Cárdenas (2000) also find unraveling in CPR games. The
unraveling of cooperation has been reported in public good experiments as well. The earliest reports are in
Kim and Walker (1984), and in Isaac, McCue and Plott (1985). See Fehr and Gaechter (2000) for a more
recent treatment of the subject.
4
Fitting our model to the experimental data we find that most selfish players
internalize the norm (i.e. they adopt a cooperative type) after the experimenter
prescribes extracting one token. We also find that fewer people internalize the norm
when it is enforced: it is as if enforcement relieved people from the guilt of infringement.
A similar effect was observed by Gneezy and Rustichini. In their experiment, the
imposition of a fine alleviated the parent’s guilty feelings. But, as parents knew
beforehand that it was their duty to pick up their children on time, the prescriptive effect
was absent. The result was a crowding out of cooperation. In our experiment, both
effects act simultaneously. The prescriptive effect dominates the guilt relief effect, so
cooperation crowds in.
Finally, our study reveals that a player who cooperates conditionally under no
fine is likely to cooperate unconditionally when a fine is in force. This is probably
because the fine relieves her of the desire to retaliate against uncooperative players in
the only way she can: by ceasing to cooperate herself.4
Our findings solve the two puzzles in the experimental results: the increase and
later erosion of cooperation when commoners vote against the imposition of a fine, and
the high deterrence power of low fines. When fines are rejected, moralization explains
the increased cooperation; violations (accidental or not), coupled with reciprocal
preferences, account for the erosion. Low fines, on the other hand, induce players to
cooperate irrespective of the behavior of their peers. A spiral of negative reciprocation is
prevented and, as a result, cooperation becomes stable.
4
Andreoni (1995) advanced a similar hypothesis in the context of public good games.
5
2.
A MODEL OF COMMON POOL RESOURCE GAMES
N persons play a finitely repeated common pool resource (CPR) game. The
game is repeated T times. At the beginning of each round, every player decides privately
how many tokens to extract from a common pool; the minimum being one token, and the
maximum xmax tokens. Let xit ∈ {1,..., xmax } be the number of tokens player i ∈ {1,..., N }
takes from the common pool in round t ∈ {1,..., T } .
A player’s payoff from extraction depends positively on the number of tokens she
extracts and negatively on the aggregate level of extraction. Denote by π ( xit , x− it ) player
i’s payoff from extraction in round t, where x−it =
1
N −1
∑
j ≠i
x jt . Function π ( xit , x− it ) is
increasing in xit and decreasing in x− it . The sum of the payoffs of all players is
maximized when they all extract the minimum amount (one token).
Assume that the social norm is to extract one token. At the end of each round, an
external authority inspects each player with probability pt ∈ [0,1) . If the authority
discovers that a player violated the social norm, he fines that player with an amount
ft ≥ 0 for every token she extracted in excess of one (the authority then casts the
collected fine into the sea). Thus, the expected material payoff of player i in round t is
π ( xit , x− it ) − pt ft ⋅ ( xit − 1) .
There are three types of players: selfish (S), unconditional cooperators (UC), and
conditional cooperators (CC). A selfish player derives utility only from her own
consumption. An unconditional cooperator also enjoys consumption, but feels guilty
when she extracts more than the amount prescribed by the norm, an idea we borrow
from Bowles and Gintis (2002). Finally, a conditional cooperator enjoys consumption and
feels guilty when she infringes the norm, though her guilt diminishes as group extraction
increases. Conditional cooperators relate our model to those of reciprocal preferences,
such as Rabin’s (1993), and Dufwenberg and Kirchsteiger’s (2004). Fischbacher,
Gaechter and Fehr (2004) report conditional cooperation is the most common behavior
in one-shot public goods games, and that suggests it may also be common in CPR
6
games. The effect of diminishing guilt on norm compliance was recently explored by Lin
and Yang (2005).
Let u ( xit , x− it ,θ it ) be the utility function of player i in round t when she is of type
θit ∈ {S, UC,CC} . We define u ( xit , x− it ,θit ) as follows:
u ( xit , x− it ,θ it ) = π ( xit , x− it ) − pt f t ⋅ ( xit − 1)
− I(θ it ≠ S) β1π max
xit − 1 ⎧
x− it − 1 ⎫
⎨1 − I(θ it = CC) β 2
⎬,
xmax − 1 ⎩
xmax − 1 ⎭
where π max = 880 is the maximum material payoff a player may obtain in one round, β1
and β 2 are positive constants, and function I( s ) is 1 if statement s is true, and 0
otherwise. This means that an unconditional cooperator that extracts xmax tokens
experiences guilt equivalent to β1 times π max . A conditional cooperator feels as guilty as
an unconditional one, provided everybody else abides by the norm and extracts one
token. If β 2 > 1 and aggregate extraction is high, a conditional cooperator will enjoy
violating the norm.
We allow a player’s type to depend on institutions. We shall postpone the
definition of institutions until the next section. For now, bear in mind that institutions may
comprise such things as the enforcement of a norm by an external authority, and that
institutions may change over time. Each player is born a certain type (S, UC, or CC), and
she may only switch types when institutions change. If we denote the institution in force
during round t in round t as ωt , that means that θ it = θ i ( t −1) unless ωt ≠ ωt −1 . Denote as
q(θ | ω ) the probability that an individual will become type θ at the beginning of
institutional regime ω .
Player i will choose with higher probability those actions that give her a higher
expected utility. Let ε it be her expectation of how much other players will extract in
round t. The probability that player i will extract x tokens on round t is a logistic function
7
of her expected utilities:
Pit ( x ) =
∑
exp λ ⋅ u ( x, ε it ,θ it )
exp λ ⋅ u ( y , ε it ,θ it )
y =1
xmax
,
where λ ≥ 0 represents her tendency to maximize. If λ = 0 , the player will choose all
extraction levels with equal probability. As λ approaches infinity, the player will tend to
extract with probability one the number of tokens that maximizes her utility.
Finally, player i updates her estimate of how much others will extract as she
observes what they actually do. Player i’s expectations follow an adaptive process:
⎧ε (ωt )
ε it = ⎨
⎩φε i (t −1) + (1 − φ ) x− i (t −1)
if t = 1 or ωt ≠ ωt −1
otherwise,
where φ ∈ [0,1] measures the persistence of expectations, and ε (ω ) is an exogenous
initial expectation. Initial expectations depend on ω because a change in institutions
may induce a change in what players expect. Stochastic choice combined with adaptive
learning make our model a close cousin of Camerer and Ho’s (1999) EWA learning
model. Our work is also linked to Janssen and Ahn’s (2003), who fit an EWA learning
model to the results of two public good experiments. They find that heterogeneous
preferences are essential to account for their experimental evidence.
The steady state of xt , the mean extraction level of the group in round t, has one
important property. If there are no conditional cooperators in a group, xt has a unique
stable steady state. But, if enough conditional cooperators are added to the mix, the
reciprocal nature of their preferences may cause a second steady state to emerge (a
feature shared by other models of reciprocal preferences, like Rabin’s [1993], and Lin
and Yang’s [2005]). The intuition is simple: if conditional cooperators expect group
8
extraction to be low, they will be inclined to extract few tokens. On the other hand, if they
expect a high group extraction, conditional cooperators will tend to extract many tokens.
Hence, there will be two attracting poles of self-fulfilling expectations: one where players
cooperate a lot, and another with little cooperation.
9
3.
A COMMON POOL RESOURCE EXPERIMENT
In our common pool resource (CPR) experiment all subjects were adult villagers
from five communities in Colombia. The communities exploited a common resource,
such as fish or water. To control for the effect of kin altruism, no two members of the
same household were admitted into the same experimental group.
Here we briefly describe the experiment and discuss its results.
3.1
5
Experimental design
Groups of five persons ( N = 5 ) play the CPR game of the previous section. The
game is repeated twenty times ( T = 20 ), and the players know the number of repetitions
beforehand. In each round every player decides privately how many tokens to extract
from a common pool; the minimum being one token, and the maximum, eight ( xmax = 8 ).
The experimenter then informs players of the aggregate level of extraction, but does not
reveal individual levels. Player i’s payoff from extraction in round t is given by
5
2
π ( xit , x− it ) = 800 + 40 xit − xit2 − 80 x− it .
A simple calculation shows that a player maximizes her material payoff by extracting
eight tokens. The aggregate payoff, on the other hand, is maximized when each player
extracts only one. After the final round players cash their tokens. Prizes range between
one and two days’ wages.
At the end of round 10 the experimenter may introduce the following sanction
mechanism: after each round he will randomly inspect one player; if he discovers that
the player took more than one token, he will fine her in private. The experimenter may
force the sanction mechanism on the players, or let them vote on it. In either case, he
first explains to the players that having a fine is in their interests because it discourages
5
See Cárdenas (2004) for a detailed description of the experiment.
10
extracting more than one token, and because when everybody extracts only one token
the material welfare of each player is maximized.
We identify four institutions:
NF: No fine has ever been imposed on, or approved by, the players.
HF: A high fine regime is in force.
LF: A low fine regime is in force.
RF: A fine regime was proposed to, and rejected by the players.
We do not distinguish between fines imposed by the experimenter and fines
approved by player vote, because the distinction made no difference to the behavior of
the players.6 Since the experimenter may affect the preferences of players when he
proposes a fine and they vote against it, we do distinguish between the no fine (NF) and
the rejected fine (RF) regimes.
Let f (ω ) be the fine in force when the institution is ω :
if ω ∈ {NF,RF}
⎧0
⎪
f (ω ) = ⎨175 if ω = RF
⎪50 if ω = LF.
⎩
The
expected
material
payoff
π ( xit , x− it ) − 15 f (ωt ) ⋅ ( xit − 1) , where
of
1
5
player
i
in
round
t
is
therefore
is the probability she will be inspected.
Sixty-four groups of players received one of four different treatments:
Control: (8 groups) The institution is NF for all twenty rounds.
6
We performed two Kruskall-Wallis tests on the hypothesis that mean extraction levels are the same under
voted fines and under externally-imposed fine regimes. The test for high fines produced a p-value of 0.78.
The test for low fines produced a p-value of 0.80.
11
High fine: (14 groups) The institution is NF for the first ten rounds, and HF for
the last ten rounds.
Low fine: (26 groups) The institution is NF for the first ten rounds, and LF for the
last ten rounds.
Rejected Fine: (16 groups) The institution is NF during the first ten rounds, and
RF for the last ten rounds.
The standard prediction for this version of the CPR game is its subgame perfect
equilibrium. Table 1 summarizes the predictions for each institution. According to the
predictions, only a high fine should have enough deterrence power to reduce individual
extraction to its socially optimal level. Note that the equilibrium levels of extraction are
close to, or coincide with, either the minimum or the maximum number of tokens that
players are allowed to extract. This is intended to reduce the confusion that may arise
among players if the optimal levels of extraction were interior solutions. Also, in the case
of the low fine and the rejected fine institutions, the equilibrium extraction levels are far
above the socially optimal level (one token). Thus, if one observes players complying
with the social norm, one should feel less inclined to deem their compliance a mistake.
Institution
Predicted extraction
No fine
8
High Fine
1
Low Fine
6
Rejected Fine
8
Table 1: Predicted levels of extraction.
3.2
Results of the CPR experiment
Figure 1 displays the aggregate behavior of players under each treatment. Note
that:
1. Groups start at low levels of cooperation, extracting about 4.5 tokens on average.
The mean level of extraction remains fairly constant during the first 10 rounds. In
12
the control treatment, extraction stays around 4.5 tokens until the end of the
game.
2. Under all treatments other than the control, cooperation increases on round 11.
The social optimum, however, is never reached. Nonetheless, extraction falls
even when the players vote against the fine.
3. Cooperation remains high after round 11 only when a fine, be it high or low, is in
force. If the players reject the fine, cooperation slowly unravels.
MEAN LEVEL OF EXTRACTION
6
5
4
3
NO FINE
HIGH FINE
2
LOW FINE
REJECTED FINE
1
1
3
5
7
9
11
13
ROUND
15
17
19
Figure 1: Experimental results, aggregate behavior.
Compare the results of the experiment with the predictions of Table 1. According
to the predictions, initial extraction levels should be 60% higher than they actually are.
Under the high fine, extraction should drop to one. Instead, it stays over two. We
expected a low fine to exert little deterrence. However, the low fine and the high fine
work almost as well. A rejected fine should have no effect whatsoever, but surprisingly it
has.
Table 2 shows mean extraction levels under each institution, along with group
and individual deviations from the mean. The high individual deviations suggest that
players randomize or experiment.
13
Institution
No fine
High fine
Low Fine
Rejected fine
Mean extraction
4.6
2.3
2.7
3.7
Group deviation
2.3
1.9
2.1
2.3
Average individual dev.
1.8
1.0
1.2
1.8
Table 2: Summary statistics from the CPR experiment.
Figure 2 shows histograms of individual extraction levels under different
treatments. Under both fine treatments extraction is concentrated in the vicinity of one
token. The histogram representing the no fine treatment is almost flat. If all players were
identical, that would imply that they choose strategies completely at random, as if
indifferent to material payoffs. A complementary explanation for the flatness is that
players are heterogeneous along the moral dimension: some feel strongly that they
should not take more than one token; others have no qualms and maximize their
material payoff by taking eight. Also note how the histograms that represent the rejected
fine treatment get flatter on rounds 15 and 20, as cooperation deteriorates.
14
60%
60%
NO FINE
40%
REJECTED FINE, t = 11
50%
HIGH FINE
FREQUENCY
FREQUENCY
50%
LOW FINE
30%
20%
10%
REJECTED FINE, t = 15
40%
REJECTED FINE, t = 20
30%
20%
10%
0%
0%
1
2
3
4
5
6
7
8
1
2
AMOUNT EXTRACTED
3
4
5
6
7
8
AMOUNT EXTRACTED
Figure 2: Experimental results, distribution of individual extraction levels.
The unraveling process is better understood by examining, one by one, the
groups that rejected a fine. Figure 3 shows four such groups. Group 1 extracts a high
amount from the first period until the end. Groups 2, 3, and 4 initially extract a low
amount, but only group 4 cooperates until the last round. The most common pattern of
behavior is represented by groups 2 and 3: both start by cooperating, but somewhere
along the way they abruptly cease cooperating (first group 2 and later group 3). The
smooth, concave line representing the rejected fine treatment in Figure 1 results from
averaging many groups like 2 and 3.
MEAN LEVEL OF EXTRACTION
8
GROUP 1
7
GROUP 2
GROUP 3
6
GROUP 4
5
4
3
2
1
11
12
13
14
15
16
ROUND
17
18
19
20
Figure 3: Experimental results, groups that voted against a fine.
15
4.
MODEL ESTIMATION AND SIMULATION
We used maximum-likelihood to estimate the parameters of our model: λ , β1 ,
β 2 , φ , ε ( ⋅ ) , and q( ⋅ | ⋅ ) (see the Appendix for a detailed account of the estimation
procedure). Recall that λ is the players’ tendency to maximize, β1 and β 2 determine
the social preferences of cooperators, ε (ω ) is the initial expectation of players under
institution ω , constant φ measures the persistence of expectations, and q(θ | ω ) is the
probability that an individual will become type θ at the beginning of institutional regime
ω . We based our estimations on the outcomes of the first 19 rounds of play, and left the
final round to test the predictive accuracy of our model.
To simplify estimation, we made two assumptions regarding initial expectations:
1. If ω ∈ {NF,HF,LF} , ε (ω ) coincides with a stable steady state of xt =
∑
N
x
i =1 it
under institution ω . Two conditions must hold for ε (ω ) to be a stable steady
state. First, the average level of player extraction when they expect others to
extract ε (ω ) must coincide with ε (ω ) . That is, the following condition must hold:
⎧
xmax
x exp λ ⋅ u ( x, ε [ω ],θ ) ⎫⎪
⎪
q
(
θ
|
ω
)
⎬ − ε (ω ) = 0
∑θ ⎨
∑
xmax
⋅
exp
λ
u
(
y
,
ε
[
ω
],
θ
)
x
=
1
⎪⎩
⎪⎭
∑ y =1
Second, the derivative of the left hand side of the equation with respect to ε (ω )
must be negative.
2. If ω = RF , ε (ω ) is a convex combination of the stable steady states of xt .
The first assumption is justified by the fact that mean extraction levels remain
fairly constant through all rounds under the no fine, high fine and low fine institutions
(see Figure 1). With assumption number two we intend to capture the confusion that may
16
arise among players when there is more than one steady state (as Figure 3 suggests).
Table 3 displays the estimated values of λ , β1 , β 2 , and φ . Table 4 displays the
estimated distribution of types, q( ⋅ | ⋅ ) , under each institution. Finally, Table 5 displays
the estimated initial expectations.
Parameter Estimate
Parameter Estimate
λ
0.0030
(0.0007)
β1
4.00
(2.45)
φ
0.50
(0.03)
β2
4.00
(0.00)
Table 3: Estimated parameters: λ , β1 , β 2 , and φ . Standard errors in parentheses.
Player types (θ)
Institution ( ω )
No fine
High fine
Low Fine
Rejected
fine
88%
(2%)
20%
(2%)
21%
(5%)
2%
(2%)
Unconditional 7%
Cooperators
(2%)
63%
(7%)
57%
(2%)
30%
(6%)
Conditional
Cooperators
17%
(9%)
22%
(8%)
67%
(4%)
Selfish
5%
(1%)
Table 4: Estimated distribution of types, q(θ | ω ) . Standard errors in parentheses.
Institution ( ω )
No fine
High fine
Low Fine
Rejected
fine
4.7
2.0
2.4
2.2
Stable steady states 4.7
2.0
2.4
1.7; 5.8
ε (ω )
Table 5: Estimated initial expectations and implied stable steady states.
Perhaps the most striking result is the effect the institutional environment has on
the distribution of types (Table 4). Under the no fine institution, only 12% of the players
are cooperative. When a fine (high or low) is in force, the percentage rises to 80%, and
17
to 98% when the players reject a fine. Also, our results reveal that the enforcement of
the norm induces more players to cooperate unconditionally: unconditional cooperators
are 30% when a fine is rejected, and approximately 60% when a fine (high or low) is in
force.7 We hypothesize that fines relieve the cooperative player of the desire to retaliate
against uncooperative ones in the only way she can: by ceasing to cooperate herself.
Table 5 also shows the stable steady states of xt implied by the estimated
parameters under each institutional environment. There is a unique stable steady state
under the no fine, high fine and low fine institutions. That explains why players subject to
those institutions rapidly cluster around the long run value of xt : where equilibria are
unique, there is little scope for confusion. On the other hand, xt has two stable steady
states when players vote against the imposition of a fine. In that scenario, the
intervention of the experimenter at the end of round 10 plays two complementary roles:
moralizing players and coordinating expectations. In Schelling’s (1960) terms, the
experimenter makes the low extraction equilibrium a focal point8. The unraveling of
cooperation is the transition from the high cooperation equilibrium to the low cooperation
one.
Our findings solve the two puzzles in the experimental data: the increase and
later erosion of cooperation when commoners vote against the imposition of a fine, and
the high deterrence power of low fines. When players reject a fine, the internalization of
the social norm “extract only one token” explains the increased cooperation; violations
(accidental or not), coupled with reciprocal preferences, account for the unraveling. Low
fines stabilize cooperation by preventing a spiral of negative reciprocation: when the
norm is enforced, cooperation tends to be unconditional, and that eliminates the high
extraction steady state that arises when the norm is prescribed but not enforced.
Because the imposition of a low fine may moralize selfish players and induce
7
These results are robust. We made 100 bootstrap estimations of the model, taking each group history as
an independent observation. In all estimations we found that: q(S | NF) > q(θ | ω ) for all ω ∈ {HF,LF,RF} ,
q(S | RF) < q(θ | ω ) for all ω ∈ {NF,HF,LF} , and q(CC | RF) > q(CC | ω ) for all ω ∈ {HF,LF} .
8
McAdams and Nadlery (2005) study coordination in a hawk-dove game. They find, as we do, that
externally imposed norms signal focal points.
18
unconditional cooperation, the “fine enough or don't fine at all” policy prescription of Lin
and Yang (2005) must be qualified.
To test the descriptive accuracy of our model, we simulated each treatment 500
times, using the estimated parameters as inputs. Figure 4 displays the aggregate
behavior of players under each treatment, actual and simulated. Table 6 shows mean
extraction levels under each institution, along with group and individual deviations from
the mean; the table pairs actual and simulated values. Figure 5 compares the actual and
simulated histograms of individual extraction. The results of the experiment and the
output of the simulation are extremely similar. Our model provides good account of the
player's behavior, at both the group and the individual level.
Institution
Mean extraction
Group deviation
Average individual
deviation
No fine
High fine
Low Fine
Rejected
fine
Actual
4.6
2.3
2.7
3.7
Sim.
4.7
2.1
2.6
3.6
Actual
2.3
1.9
2.1
2.3
Sim.
2.4
1.9
2.3
2.9
Actual
1.8
1.0
1.2
1.8
Sim.
2.0
1.0
1.2
1.5
Table 6: Summary statistics, actual and simulated, from the CPR experiment.
19
6
6
5
5
4
4
3
3
EXPERIMENT
OUR MODEL
2
2
RESTRICTED MODEL
99% CONFIDENCE INTERVAL
1
1
3
5
7
9
11
13
15
1
17
1
19
3
5
7
ROUND
9
11
13
15
17
19
13
15
17
19
ROUND
a) No fine.
b) High fine.
6
6
5
5
4
4
3
3
2
2
1
1
1
3
5
7
9
11
13
15
17
1
19
3
5
7
9
11
ROUND
ROUND
c) Low fine.
d) Rejected fine.
Figure 4: Mean levels of extraction, actual and simulated.
20
70%
70%
EXP ERIM ENT
60%
60%
OUR M ODEL
50%
50%
40%
40%
30%
30%
20%
20%
10%
10%
0%
0%
1
2
3
4
5
6
7
8
1
2
A M OUNT EXTRA CTED
3
4
5
6
7
8
7
8
7
8
A M OUNT EXTRA CTED
a) No fine.
b) High fine.
70%
70%
60%
60%
50%
50%
40%
40%
30%
30%
20%
20%
10%
10%
0%
0%
1
2
3
4
5
6
7
8
1
2
A M OUNT EXTRA CTED
3
4
5
6
A M OUNT EXTRA CTED
c) Low fine.
d) Rejected fine, round 11
70%
70%
60%
60%
50%
50%
40%
40%
30%
30%
20%
20%
10%
10%
0%
0%
1
2
3
4
5
6
7
8
1
A M OUNT EXTRA CTED
2
3
4
5
6
A M OUNT EXTRA CTED
f) Rejected fine, round 20
e) Rejected fine, round 15
Figure 5: Distribution of individual levels of extraction, actual and simulated.
21
Next, we re-estimated our model subject to the restriction that preferences are
not
state-dependent
(i.e.
q(θ | NF) = q(θ | HF) = q(θ | LF) = q(θ | RF) ,
for
all
θ ∈ {S, UC,CC} ).9 Using a likelihood ratio test we were able to reject, at a 99%
confidence level, the hypothesis that the distribution of types does not change across
treatments.
10
We also simulated the restricted model, using estimated parameters as
inputs, and it was unable to accurately mimic the experimental evidence (see Figure 4).
Finally, we used our model and the restricted model to predict the amount
extracted by each of the 320 experimental subjects in the last round of play. To predict
the extraction of one player, we used the posterior probability of that player being of type
θ ∈ {S, UC,CC} given the priors in q(θ | ω ) , and the behavior of the player and of the
other members of his group during the first 19 rounds of play. Table 7 displays the mean
prediction errors for both models under each institution. Our model outperformed the
restricted model in all scenarios. We conclude that, in our CPR experiment, institutions
influenced the social preferences of players.
Institution
No fine
High fine
Low Fine
Rejected fine
0.75
0.71
0.68
0.86
Restricted model 0.81
0.78
0.79
0.92
Our model
Table 7: Mean errors of prediction for our model and for a model without statedependent preferences.
9
Estimated
parameters
for
the
restricted
model:
λ = 0.003 ,
β1 = 4.5 ,
β 2 = 4.25 , φ = 0.5 ,
q(S | NF) = q(S | HF) = q(S | LF) = q(S | RF) = 11% ,
q(UC | NF) = q(UC | HF) = q(UC | LF) = q(UC | RF) = 29% ,
ε (NF) = 5.7 ,
ε (HF) = 1.7 ,
ε (LF) = 1.8 ,
ε (RF) = 2.2 .
10
The log-likelihoods of the unrestricted and restricted models are LU = −11467,14 and LR = −12202.57 .
The likelihood ratio statistic is 2(LU − LR ) = 1470.86 > χ 62 (.99) = 16.81 , so we reject the hypothesis.
22
5.
CONCLUDING REMARKS
Authorities may influence social preferences when they prescribe and enforce
social norms. We found, in a CPR experiment, that the external imposition of a norm
affected preferences in two ways.
First, by moralizing players. A speech by the experimenter sufficed to induce
players to cooperate. How? By sowing in them the seed of guilt. Aristotle argued in his
Nichomachean Ethics that effective laws worked by inculcating habits in citizens, that is,
by moralizing them.11 Our results remind us that his argument is still relevant today.
Second, our model revealed that the enforcement of the norm affected the nature
of moral sentiments. If the norm was enforced, players tended to comply with it
irrespective of how others behaved. But if enforcement was absent, players conditioned
their compliance on the good behavior of their peers.
Our results also bring attention to the dynamic effects of enforcement.
Conditional cooperation makes compliance fragile: a single rotten apple may spoil the
whole box (and the addition of many good apples cannot restore it). In the experiment, a
small fine sufficed to stabilize cooperation by making more players cooperate
unconditionally, preventing the spread of moral degradation. Consider the implications
for governmental corruption. Corrupt officers are hard to detect, so the expected
punishment is often small compared to the potential gains from corruption. The
occasional jailing of corrupt officers may nonetheless stabilize moral behavior. Weak
enforcement may prevent officers from thinking “everybody else is doing it, so why can't
we?”
Further research is needed to determine when the enforcement of a norm will
shield moral behavior from resentment or from “bad examples.” For instance: sanctions
were weakly enforced in our experiment, but they were fair. If some commoners were
made immune to punishment, punishment might cease to quench feelings of revenge; it
would no longer serve to stabilize cooperation. Similarly, even if few people are beyond
the reach of the law, the law may lose its effectiveness.
11
The word moral stems from Latin moralis, meaning custom.
23
The way a low fine sustains cooperation may be analogous to the way the yellow
card keeps the peace on a football field. Without the card, violence escalates after the
first kick to the shin; it makes no difference if the kick was intentional or accidental.
Perhaps the card gives players the sensation that bad behavior does not always go
unpunished, and that suppresses the impulse to seek their own justice. Being close
substitutes for reciprocation, low fines and yellow cards may sometimes stabilize norm
compliance in a world of feeble social order.
24
REFERENCES
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26
APPENDIX: ESTIMATION PROCEDURE
Here we describe how we estimated the parameters of our model and its version
without state-dependent preferences. First, we grilled the parameter space and restricted
the search to that grill (see Table 8).
Parameter
Grill
λ
0.0005, 0.0010,…, 0.0175, 0.0200
β1 , β 2
0.25, 0.50,…, 9.75, 10.00
φ
0.00, 0.25, 0.5, 0.75, 1.00
q(θ | ω )
0.00, 0.01,…, 0.99, 1.00
ε (ω )
1.0, 1.1,…, 7.9, 8.0
Table 8: Parameters grill.
We imposed three more restrictions to the candidate estimates of the parameter
vector Θ = [ λ , β1 , β 2 , φ , q( ⋅ | ⋅ ), ε ( ⋅ | ⋅ ) ] . These restrictions are:
1. If ω ∈ {NF,HF,LF} , ε (ω ) coincides with a stable steady state of xt = ∑ i =1 xit
N
under institution ω .
2. If ω = RF , ε (ω ) is a convex combination of the stable steady states of xt .
3. The candidate parameter vector should be able to reproduce the unravelling of
cooperation under the rejected fine institution. To verify this restriction, each
candidate parameter vector to simulate the rejected fine institution 500 times. We
then checked that the simulated mean levels of extraction over ten rounds of play
were within the 99% confidence intervals calculated from the experimental data
(the confidence intervals are displayed in Figure 4d).
In the case of the model without state-dependent preferences, we added an
additional
restriction:
that
q(θ | NF) = q(θ | HF) = q(θ | LF) = q(θ | RF) ,
27
for
all
θ ∈ {S, UC,CC} .
Finally we evaluated the log-likelihood function of the model with every candidate
parameter vector that satisfied the aforementioned restrictions, and selected the
parameter vector that produced the higher value.
28